The numbers $a$, $b$, and $c$ in a quadratic equation like $y = ax^2 + bx + c$ really change how its graph looks.

1. Coefficient $a$:

   • This number decides which way the parabola (the U-shaped curve) opens.
   • If $a$ is greater than 0, it opens up. If $a$ is less than 0, it opens down.
   • Example: For $y = 2x^2$, the parabola opens upwards.

2. Coefficient $b$:

   • This number affects where the highest or lowest point (called the vertex) of the graph is.
   • It can move the graph to the left or right.
   • Example: In $y = x^2 - 4x$, the vertex has moved because of $b$.

3. Coefficient $c$:

   • This number tells you where the graph touches the y-axis (the vertical line).
   • It's called the y-intercept.
   • Example: In $y = x^2 + 3$, the graph touches the y-axis at the point (0, 3).

By looking at these three numbers, you can guess what the shape and position of the quadratic graph will be!